[KrappyKroger]

I know these are quite rare these days, but I'd like to play an MMORPG that isnt p2w and is relatively budget friendly. 

Some that come to mind are B&S and maybe GW2?

[Wrangler]

You could try SWOTR, Path of Exile, the Lord of the Rings MMO, and I'm sure there's a few I'm missing but those should be a good start

[CrookedToothNarwhal]

The Elder Scrolls Online game is pretty affordable when on sale, it's not F2P yet but not subscription either. There's also Star Trek Online and Neverwinter, which are F2P proper.

[reegna]

Neverwinter definitely, I went all the way to max level not only F2P but also solo-ing, if you're OK with just playing the base and 1st expansion to the very end, FFXIV Free Demo is also great.
I heard good things, story wise, about Star Wars: The Old Republic so maybe try that too.

[zap_b]

why not checking some free games? i guess there are some out there...

[BluKlappin]

SWTOR, Vindictus (if you do not mind pay to look good aka not paying at all and looking decent at higher levels), and potentially FFXIV demo (as someone above mentioned) for the free content then decide from there whether to pay or not